We approach the problem as follows.
In section , we give the field equations of \(f(R)\)  gravity and
the
junction conditions for smooth matching of the interior and
the exterior spacetimes across the timelike hypersurface \(\Sigma \) .
This section also includes the solutions of the \(f(R)\)  field equations
along with
the explicit expressions
for physical quantities. For the solution, we use
the Karmarkar condition [1]}, [2]}, [3]}.
These conditions determine
gravitational potentials for static and non- static systems
[4]}, [5]}, [6]}, [7]}.
We must mention here that similar studies on \(f(R)\)  gravity have
been carried out in [8]}. However,
the solutions obtained there are restrictive in the sense that one of
the metric function have been kept constant to derive the values of
other metric function. On
the other hand we shall show that such conditions are overly restrictive.
Note that since Karmarkar condition expresses relationship between
metric functions, the forms of metric functions are arbitrary, and
dependent on
one's choice. However we argue that this arbitrariness
may be removed if metric functions are related
to matter variables. For example, if we assume a
specific form of pressure anisotropy (difference of the radial and
tangential pressures, denoted by \(\Delta =p_{t}-p_{r}\) ), this
gives rise to unambiguous set of gravitational potentials, and a class
of metric representing collapsing spacetimes. We inspect
the physical relevance of these exact solutions by verifying the energy
conditions. The stability criteria and discussion about the luminosity and
adiabatic index, radial and transverse velocity are carried out in
section REF . It is shown that a faraway observer will see a source
whose luminosity is exponentially increasing until a time
when it shuts off quickly. This is due to the fact that
the total mass of the star radiates linearly and, as the star reaches
its maximum luminosity there is no mass left to radiate. The evolution
of the temperature profiles during stellar collapse is also studied in
section REF 
since they play an important role in the study of transport processes
in radiative gravitational collapse [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}.
In section  contains discussion of the results
accompanied with concluding remarks.
